Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON):

Solution:

from bisect import bisect_left

if __name__ == '__main__':
    n = int(raw_input())
    i = 1
    t = 2
    a = [2]
    mid = 0

    while t < n * 2:
        i += 1
        t = i * (i + 1)
        a.append(t)
        if t <= n:
            mid = i

    for i in a[:mid + 1]:
        pos = bisect_left(a, n * 2 - i)
        if pos != len(a) and a[pos] == n * 2 - i:
            print 'YES'
            break
    else:
        print 'NO'